What Must Adds. Matthew Mandelkern All Souls College, Oxford. October 1, Abstract

What Must Adds Matthew Mandelkern All Souls College, Oxford October 1, 2018 To appear, Linguistics and Philosophy Abstract There is a difference between the conditions in which one can felicitously use a must - claim like (1-a) and those in which one can use the corresponding claim without the must, as in (1-b): (1) a. It must be raining out. b. It is raining out. It is difficult to pin down just what this difference amounts to. And it is difficult to account for this difference, since assertions of Must p and assertions of p alone seem to have the same basic goal: namely, communicating that p is true. In this paper I give a new account of the conversational role of must. I begin by arguing that a must -claim is felicitous only if there is a shared argument for the proposition it embeds. I then argue that this generalization, which I call Support, can explain the more familiar generalization that must -claims are felicitous only if the speaker s evidence for them is in some sense indirect. Finally, I propose a pragmatic derivation of Support as a manner implicature. 1 Introduction Consider the following sentences: I thank two anonymous referees for this journal, and my editor, Paul Portner, for very helpful comments. Thanks to Joshua Knobe and Jonathan Phillips for invaluable help running and analyzing the experiment reported here, and to Justin Khoo and MIT for financial support for the experiment. This paper expands on Mandelkern 2017b, and I also thank my referees and audience at Sinn und Bedeutung 21; audiences at MIT, the University of Chicago, NYU, St. Andrews, and Hampshire College; and Justin Bledin, David Boylan, Agnes Callard, Nilanjan Das, Janice Dowell, Daniel Drucker, Kai von Fintel, Vera Flocke, Irene Heim, Matthias Jenny, Brendan de Kenessey, Justin Khoo, Angelika Kratzer, Daniel Lassiter, Rose Lenehan, Sarah Murray, Dilip Ninan, Jacopo Romoli, Bernhard Salow, Ginger Schultheis, Brett Sherman, Alex Silk, Daniel Skibra, Robert Stalnaker, Matthew Stone, Eric Swanson, Roger White, and Stephen Yablo for very helpful comments and discussion. 1

(2) a. It must be raining out. von Fintel and Gillies 2010 b. It is raining out. Intuitively, an assertion of (2-a) and an assertion of (2-b) have the same basic communicative aim: namely, to communicate that it is raining out. Once an assertion of (2-a) has been accepted, interlocutors are disposed to accept that it is raining out, as witnessed by the oddness of (3): (3)??It must be raining; and moreover, it is raining. Thus (2-a) seems to be as strong as (2-b). But it does not seem to be stronger than (2-b): it is very strange to assert (2-a) after (2-b) is already accepted, as witnessed by the oddness of (4): (4)??It s raining; and moreover, it must be raining. This suggests that assertions of (2-a) and (2-b) carry the same basic information. Yet the conditions in which they can be felicitously asserted differ in subtle ways. Suppose that Jane is in a windowless room, and sees her colleagues come in with wet umbrellas. Then she can assert either (2-a) or (2-b). But now suppose that Jane is looking out a window at the rain. She can still assert (2-b), but an assertion of (2-a) It must be raining out would be decidedly odd. Generally speaking, there is a systematic difference between the conditions in which one can felicitously assert a must -claim with complement p, versus the conditions in which one can felicitously assert p alone. 1 Accounting for these differences is a challenge known as Karttunen s Problem; 2 the goal of this paper is to propose a solution to this problem. The argument of the paper comes in three parts. I begin by trying to get clear on the data: what the difference in felicity conditions between sentences like (2-a) and (2-b) amounts to. The main claim in the literature, which I call Indirectness, is that a must -claim is felicitous only if the speaker s evidence for its prejacent is indirect, whereas its bare prejacent can be asserted whether the speaker s evidence is direct or indirect. I argue that, while Indirectness is, suitably spelled out, correct, there is another, equally important, generalization which plays a key role in solving Karttunen s Problem: namely, that a must -claim is signficantly degraded unless the speaker ensures there is a salient argument in support of the claim s prejacent. I call this constraint Support. Then I show that once we have Support clearly in sight, we can derive Indirectness through general pragmatic reasoning. This reasoning reduces our judgments about the indirectness of must to judgments about when a sequence of assertions is redundant. Finally, I give a Gricean account of why Support arises in the first place. 1 A must -claim is a claim containing an unembedded and unrestricted strong epistemic necessity modal such as must, it can t be, etc., read epistemically. I use must as an exemplar of such modals, but my claims here are about strong epistemic necessity modals in general. I use p as a sentence variable; p denotes the proposition expressed by p (suppressing implicit relativization to contexts for readability). 2 Following von Fintel and Gillies (2010), who credit Karttunen (1972) with bringing the issue to attention. 2

2 Data I begin by trying to get clear on the difference in felicity conditions between assertions of Must p and p. 2.1 Indirectness The main claim in the literature is that the difference amounts to an indirectness constraint: 3 Indirectness: Asserting Must p is felicitous only if the speaker s evidence for p is indirect. By contrast, of course, a non-modal claim can be felicitous whether the speaker s evidence is direct or indirect. Indirectness is motivated with cases like (5) and (6): (5) [Watching the rain:] a.??it must be raining. b. It s raining. (6) [Seeing your colleagues enter with wet umbrellas:] a. It must be raining. b. It s raining. (5-a) is distinctly weird as compared with (5-b), (6-a), and (6-b). Indirectness is the most natural generalization to draw from data like these. Indirectness has been well-motivated in the literature, and so I will assume without further discussion that some precisification of the principle is correct. More, of course, needs to be said about what counts as indirect here, as well as about the source of Indirectness, both questions which I return to below (see 3.4 in particular). For now, though, note that I do not assume that the concept of indirectness which plays a role in Indirectness neatly matches pre-theoretic intuitions about whether evidence is direct or not. 4 For instance, reliable testimony is (according to some intuitions) indirect evidence; but, as von Fintel and Gillies (2010) observe, we must treat it as direct when it comes to evaluating Indirectness, in order to predict the contrast between (7-a) and (7-b): 3 The insight goes back to Karttunen 1972. See von Fintel and Gillies 2010; also Veltman 1985; Kratzer 2012a; Matthewson 2015; Ozturk and Papafragou 2015; Lassiter 2016; Sherman 2018. Giannakidou and Mari (2016); Goodhue (2017) both argue that this empirical generalization is better explained in terms of partial knowledge, rather than indirectness; but they both still, as far as I can tell, endorse the generalization when understood in a sufficiently broad way, as intended here. As I emphasize in a moment, I am leaving the notion of indirectness intentionally broad and vague here; in what follows, I will propose one particular way of cashing it out, a way which, of course, not all these writers would necessarily endorse. 4 Or categories which are encoded as grammatical markers of evidentiality in some languages; see e.g. Willett 1988; Faller 2002; Aikhenvald 2004. 3

(7) [Tom tells Susie that it is raining. Susie says to Mark:] a.??it must be raining. b. It s raining. 2.2 Support Most of the literature on Karttunen s Problem has focused exclusively on Indirectness. But a different thread in the literature has pointed to a further contrast in felicity conditions: in making a must -claim, the speaker must ensure that an argument for its prejacent is salient to all the interlocutors. I call this claim Support: Support: Must p is degraded unless there is an argument for p salient to the interlocutors and endorsed by the speaker. By contrast, Must p can be felicitous when an argument for p is given. And non-modal claims, or modal claims with weaker epistemic modals ( might, should, etc.) can be felicitous with or without an argument. The key insight in Support is due to Stone (1994). The claim, however, has not received much discussion in the subsequent literature. 5 And indeed, the data that motivate Support are somewhat less clearcut than those that motivate Indirectness. This is not surprising: it can be difficult to determine, in a given context, whether an argument has been made salient. This requires evaluating discourses as a whole, and it requires considering whether an argument has been introduced either by linguistic means or through (possibly tacit) shared background knowledge or accommodation. In the remainder of this section, I will adduce a variety of data to argue that Support is indeed required to account for the difference in felicity conditions between Must p and p, as well as the difference in felicity conditions between Must p and modal claims of other strengths. I begin by considering a variety of cases which bring out the need for Support. Consider first (8): (8) [Patch the rabbit sometimes gets into the cardboard box where her hay is stored. On his way out the door, Mark hears a snuffling from the box and thinks to himself, Patch must be in the hay box. When he gets to school, Bernhard asks him how Patch is doing.] a. [Mark:]?? She s great. She must have gotten into the hay box this morning. b. [Bernhard:] Cute! Suppose the conversation ends here, and assume that Bernhard doesn t know anything about Patch s set-up at Mark s house, or in general anything which might help him figure out why Mark thinks that Patch was in the box of hay. There is something distinctly odd about this 5 It is taken up briefly in Murray 2014, Silk 2016, Swanson 2015, and Lassiter 2016. 4

exchange. Intuitively, what Mark has said needs more elaboration; either Mark should have proffered reasons to think that Patch was in the hay box, or Bernhard should have asked him for reasons, perhaps by saying, Why do you say that? Here is a more felicitous version of Mark s assertion in (8): (9) She s great. I heard a snuffling from the box of hay on my way out she must have gotten into the box. Now suppose the conversation ends here. This exchange has none of the peculiarity of (8). What does this show? First, note that a non-modal variant of (8) is perfectly fine: (10) a. [As in (8), except Mark says:] She s great. She got into the box of hay this morning. b. [Bernhard:] Cute! The non-modal variant on (9) is likewise fine. The infelicity of (8) thus seems to be due to the use of must. But note that Mark s evidence regarding Patch s whereabouts is exactly the same in (8) as in (9). Moreover, Indirectness is satisfied Mark s evidence about Patch s whereabouts is indirect so Indirectness cannot explain the contrast between them. By contrast, Support predicts precisely the pattern we observe: namely, that (8) will be relatively degraded since no argument for the prejacent is made salient while (9) and (10) will be more acceptable. Cases like this provide our first piece of evidence for Support. Before giving further cases, I will say a bit more about what Support amounts to. First, what does an argument amount to in this context? I will treat an argument for p as a set of propositions which the speaker is commonly recognized to believe provides reason to believe p either by deductively entailing its conclusion; by inductively supporting the conclusion; or by showing how the conclusion follows from what is already accepted. Second, what does salience amount to? I won t say much about this, but a few features are worth noting. First, an argument need not itself be common ground, i.e. need not itself be commonly accepted in the conversation, to count as salient. 6 One can felicitously assert an argument conjoined with a must -claim, even if the argument has not yet been (and never is) accepted by all the speakers (if Bernhard doesn t believe me that I heard a snuffling from the box of hay, this does not render (9) infelicitous). The sense in which an argument Γ must be salient is rather that it must be common ground that the speaker takes Γ to provide reason to believe the prejacent of her must -claim, and that she is proposing to add Γ to the common ground. I will refer to an argument with this status as salient, shared, or publicly available ; I have in mind this somewhat technical sense throughout. An important point about salience is that an argument can be salient without being made 6 See e.g. Stalnaker 1970, 2002, 2014. 5

explicit, as in (11): (11) [Bernhard and Mark are in the bunny s room, and can both hear snuffling from the box of hay. Mark:] Patch must be in the hay box. Here, the premise that merits Mark s conclusion that Mark can hear snuffling from the box is salient, and the must -claim is acceptable. Another noteworthy feature of the notion of salience in question is that the argument need not be salient at the time of the assertion; it can be provided shortly after the assertion, as in (12): (12) a. [As in (8), but Mark says] Patch must have gotten into the box of hay. b. [Bernhard:] Why do you say that? c. [Mark:] I heard her snuffling around when I was leaving. A final important fact about the salient argument in question is that it must be endorsed by the speaker of the must -claim. To see this, compare the following: (13) a. Patch must have gotten into the box of hay; John told me that he heard her snuffling around in there. b.??patch must have gotten into the box of hay; John told me that he heard her snuffling around in there, though John often lies about things like that. An argument which is salient but not endorsed, as in (13-b), clearly does not satisfy Support. 2.3 More cases We find further confirmation of Support when we turn our attention to a broader range of parallel cases. Consider (14), adapted from Murray 2014: (14) [Sarah works in a windowless building. On her way to a meeting, she sees her coworker Jim enter the building, carrying a wet umbrella. Sarah concludes from this that it s raining out. Sarah enters the meeting. Her colleague Thomas, who didn t see Jim carrying a wet umbrella, asks, What s the weather like? Sarah responds:] a.??it must be raining out. b. It s raining out. c. It must be raining out; I just saw Jim come in with a soaking wet umbrella. d. It s raining out; I just saw Jim come in with a soaking wet umbrella. [Thomas replies: Oh, too bad. Ok, let s talk about the agenda for this meeting.] As Support predicts, (14-a) the variant with must, but without an argument is odd, while 6

the other variants ( must with an argument, and non-modal claims with or without an argument) are felicitous. We find a similar pattern in (15): (15) [Jane is in her first year of college. She doesn t have a clear sense of how she is doing in school. She meets with her professors, who tell her she is doing well; she thus concludes that she is doing okay. She goes in to meet with her adviser to talk about course registration. Her adviser doesn t know about the conversations she s had with her professors. Her adviser asks: So, how are you doing in your classes? Jane responds as follows:] a.??i must be doing okay! b. I m doing okay! c. I must be doing okay: I ve spoken to all my professors and they told me I m doing fine. d. I m doing okay: I ve spoken to all my professors and they told me I m doing fine. [Her adviser replies: Good, I m happy to hear that. Ok, on to our business for today: let s discuss your registration for next term. ] Again, as Support predicts, (15-a) is marked, while the other variants are fine. The next example illustrates the contrast of must -claims without an argument not only to must -claims with an argument and non-modal claims with or without an argument, but also to epistemic modal claims of other strengths (responses are labeled for ease of reference): (16) [Two friends, Scott and Mark, are discussing summer plans. Scott asks Mark: Do you think you d be free to go fishing in a few months, say in the first week of September? Mark responds:] a. [-arg, +must]?? Yeah, I must be off work that Monday. Where would you want to go? b. [+arg, +must] Yeah, that Monday is Labor Day, so I must be off work. Where would you want to go? c. [-arg, -modal] Yeah, I m off work that Monday. Where would you want to go? d. [+arg, -modal] Yeah, that Monday is Labor Day, so I m off work. Where would you want to go? e. [-arg, +should] Yeah, I should be off work that Monday. Where would you want to go? f. [+arg, +should] Yeah, that Monday is Labor Day, so I should be off work. Where would you want to go? g. [-arg, +might] Yeah, I might be off work that Monday. Where would you want to go? h. [+arg, +might] Yeah, that Monday is Labor Day, so I might be off work. Where 7

would you want to go? i. [-arg, +probably] Yeah, I m probably off work that Monday. Where would you want to go? j. [+arg, +probably] Yeah, that Monday is Labor Day, so I m probably off work. Where would you want to go? Assuming that Mark doesn t remember that the first Monday in September is Labor Day, the must -claim in (16-a) without further explanation is marked, whereas all the other variants must with an argument, as well as non-modal, should, might, and probably are perfectly acceptable as is. Two further examples illustrate an important point regarding Support: an argument can be shared even if it is not spelled out explicitly, but instead is quietly accommodated. (17) is taken from a radio show: (17) Mozart wrote the Stadler quintet for his friend Anton Stadler, who must have been a marvelous clarinetist. The announcer does not give an explicit argument that Anton Stadler was a good clarinetist, but it is easy to recover from context. Second, suppose my phone rings; I can say: (18) This must be my brother; let me take this. It is, again, easy for you to recover my reasons for saying this from the context (I must be expecting a call from my brother). (Some subtlety is required here. In general, when someone asserts Must p, you can always thereby gather from that some reason to believe p, namely, that the speaker has proposed to update with p. So the contrasts we have seen suggest that the argument needed to satisfy Support must be more substantive than just that the speaker believes p. I return to this point in 4.2.) Another piece of evidence for Support comes from naturalistic written examples. Lassiter (2016) discusses a range of examples taken from genealogical discussion boards, noting that Ancestry.com users frequently provide an explicit specification of the evidence used to arrive at a must conclusion. Here s one example, taken from The Plymouth Colony Archive Project, slightly altered to improve flow across the variants below: (19) [+arg, +must] Goodman... is listed as one of those who received land in 1623 (PCR 12: 4). However, he is not listed among those who were part of the cattle division of 1627 the year we are interested in here; he must have died before then. A variant which omits the argument for the must -claim, as in (20-a), is felt to be missing something, if nothing more is said on the subject. By contrast, a non-modal variant with or without that material sounds fine, as do variants with might and likely : 8

(20) a. [-arg, +must]?? Goodman... is listed as one of those who received land in 1623 (PCR 12: 4). However, he must have died before 1627, the year we are interested in here. b. [-arg, -modal] Goodman... is listed as one of those who received land in 1623 (PCR 12: 4). However, he died before 1627, the year we are interested in here. c. [+arg, -modal] Goodman... is listed as one of those who received land in 1623 (PCR 12: 4). However, he is not listed among those who were part of the cattle division of 1627 the year we are interested in here; he died before then. d. [-arg, +may] Goodman... is listed as one of those who received land in 1623 (PCR 12: 4). However, he may have died before 1627, the year we are interested in here. e. [+arg, +may] Goodman... is listed as one of those who received land in 1623 (PCR 12: 4). However, he is not listed among those who were part of the cattle division of 1627 the year we are interested in here; he may have died before then. f. [-arg, +likely] Goodman... is listed as one of those who received land in 1623 (PCR 12: 4). However, he likely died before 1627, the year we are interested in here. g. [+arg, +likely] Goodman... is listed as one of those who received land in 1623 (PCR 12: 4). However, he is not listed among those who were part of the cattle division of 1627 the year we are interested in here; he likely died before then. Comparing must with other words that might at first glance seem to work in a similar way, like apparently, can help bring out the plausibility of Support. Consider (21), adapted from a television spy drama: (21) a. The suspect is fleeing south. We ve sent agents ahead to Mattapan. b. Why Mattapan? (i)??the Russians must have a safe-house there. (ii) Apparently the Russians have a safe-house there. (iii) The Russians have a safe house there. (iv) The Russians might have a safe-house there. (v) The Russians probably have a safe-house there. If the conversation ends here, then (21-b-i) is peculiar in a way that the apparently, nonmodal, might, and probably variants are not. Apparently is of particular interest here, since apparently, like must, is constrained by a form of Indirectness; but apparently, unlike must, is acceptable here without an argument. 7 This helps illustrate the separability of 7 I assume that the indirectness constraint for apparently is somehow lexically encoded. An anonymous referee for this journal rightly points out that this might provide support for a divided strategy, on which Support and 9

Indirectness from Support, a point I will return to. Finally, I note that informal polling suggests the contrasts reported here seem to be robust across strong epistemic necessity modals in English (see 4.1 for further discussion of can t ) and other languages. 8 2.4 Experimental results The intuitions reported in the last section provide evidence for Support. Informal polling suggests these intuitions are robust. In this section, I present the results of an experiment which provides further support for these judgments. 301 participants were recruited from Amazon Turk (https://www.mturk.com/). All participants were based in the United States. We excluded from the analysis anyone who was not a native English speaker and anyone who completed the study in 30 seconds or less, leaving us with 273 participants. The stimuli in the experiment comprised the scenario in (16) along with the eight possible responses there, which, again, vary as to whether there was an argument or not (the argument condition) and as to whether a modal was used, and if so, which of three options must, might, or should was used (the modal condition). Each participant received the scenario, plus one of the eight possible responses, and then was asked: Please tell us how natural you think Mark s response was on the scale below. The participant responded to this prompt by dragging a marker on a continuous scale from 0 to 100, with 0 labelled completely unnatural and 100 labelled completely natural. Each participant saw four scenarios total, one from each modal condition, chosen at random within that condition as to whether or not it included an argument. The order of the scenarios was randomized. The scenario was designed so that all four modal conditions are reasonable to use as a response to Scott s question, and it was designed so that Mark s follow-up ( Where would you want to go? ) makes clear that he is moving on from his answer to the question, suggesting that further information regarding his work schedule will not be forthcoming. Support predicts that participants will find the [-arg, +must] condition degraded as compared with the seven other conditions ([+arg, +must], as well as all other modal conditions with or without an argument). Participant responses, which are summarized in Figure 1, show precisely this effect: participants found the [-arg, +must] condition substantially degraded (around Indirectness have independent sources (which may coincide, as in must, and may diverge, as for apparently ). But there is evidence that the status of the indirectness constraint for words like apparently is different from the status of the corresponding constraint for must. For instance, although reliable testimony does not count as indirect for must, it seems to for apparently. Suppose John tells us that it s hailing out. Then Apparently it s hailing out is perfectly fine. 8 Informants who confirm the predicted contrast in Bengali, French, German, Hindi, Japanese, Russian, Spanish, Swiss German, and Turkish; more careful research needs to be done to more thoroughly explore the cross-linguistic picture. 10

the mid-point on the scale of naturalness judgments), as compared with all the conditions (which were around the three-quarter point on the scale of naturalness judgments). Figure 1: Mean ratings by condition. Error bars show 95% confidence intervals. Analysis of participants naturalness ratings revealed a significant interaction between the modal condition ( must vs. should vs. might vs. non-modal) and the argument condition (F (3, 809) = 11.2, p < 0.001). To investigate the cause of this interaction effect, we separately analyzed participants ratings within each modal condition for the [+/-arg] conditions. Within the [-arg] condition, as predicted, participants found Mark s response with must to be substantially degraded around the mid-point on the scale of naturalness (Mean = 57.20, SD = 28.86) by contrast to all the other modal conditions, which they judged around the threequarters mark on the scale of naturalness (t s > 6.08, p s <.001, d s > 0.74). Things were entirely otherwise in the [+arg] condition, however, where participants found Mark s response to be quite natural (around the three-quarters mark) in all modal conditions, including the must condition. Specifically, participants found must to be significantly more natural when an argument was included (Mean = 74.55, SD = 23.51) as compared to must without an argument (t(257.9) = 5.43, p <.001, d = 0.66). Participants found the other modal conditions with an argument to be roughly equally good, again around the three-quarters mark; partici- 11

pants did not significantly distinguish must with an argument from might with an argument (t(267) = 0.51, p =.611, d = 0.06), though there was some preference for the should and non-modal variants over the must and might variants (t s > 3.97, p s <.001, d s > 0.48). In no condition other than must was there a contrast between the [-arg] and [+arg] conditions that was similar to the observed contrast in the must condition; in the other modal conditions there was some variation between the [+arg] and [-arg] condition, but this variation was small compared with the corresponding variation in judgments in the must condition (a +16.99 change in mean naturalness ratings for [+arg, +must] as compared with [-arg, +must], versus a -2.54 change for might, a +6.25 change for should, and a +8.75 change for nonmodal). These experimental results confirm the prediction of Support. They show that as the intuitions elicited throughout this section suggest must is felt to be significantly degraded without an argument. By contrast, non-modal claims, should claims, and might claims are all felt to be relatively acceptable without an argument around the three-quarters point on the scale of naturalness, as opposed to a mid-point judgment for must. And, as expected, the must variant significantly improved when an argument was added, to around the three-quarters point on the scale of naturalness roughly the same judgment as for non-modal, might, and should claims, with or without an argument. Note that the results here are graded. Speakers do not reject must statements out of hand when there is no argument, even though they find them to be substantially less good than must -claims with arguments, or other kinds of claims with or without arguments. One possible explanation of this is that it is the effect of noise in the experimental set-up. It may be, for instance, that, in responding to the stimuli, participants are assuming that Scott is able to accommodate an argument for the relevant claim: as we have seen, an argument can become salient to a speaker s audience through implicit clues or background knowledge, something which is difficult to control for in the experimental set-up. But it also may be that Support is indeed graded and in some cases relatively weak. I will not try to decide between these options here, proceeding simply with the conclusion that Support is a real signal which must be accommodated, one way or another, in our theory of must. 3 Explaining Indirectness via Support I thus conclude that Indirectness and Support are both necessary to characterize the difference in felicity conditions between a must -claim and non-modal claims, as well as weaker modal claims. 9 We now turn to the question of how to explain these data. There are three strategies to consider. We could account for Indirectness and Support separately; we could account for Support in terms of Indirectness, and give an independent account of Indirectness; or we could account for Indirectness in terms of Support, and give an independent account of Support. In the rest of the paper I will pursue the third strategy. In this section I will briefly argue against 9 I will not try to settle the important further question of whether they are jointly sufficient. 12

the first two strategies, and then show how we can naturally account for Indirectness in terms of Support. 3.1 Negative remarks Pro tanto considerations of theoretical parsimony tell against pursuing the first strategy (providing separate explanations for Indirectness and Support). What about the second strategy? This strategy is prima facie attractive, since there are a number of extant attempts to give an independent account of Indirectness; it is natural to try to recruit them to explain Support. But there are two problems with this approach. Most significantly, there does not seem to be any way to reduce Support to Indirectness. A natural first thought is that we can explain Support in terms of Indirectness by way of a general pragmatic constraint that requires a speaker to share her evidence for a claim if that evidence is indirect. But there is no such pragmatic constraint, as we saw in cases above where non-modal claims were felicitous in cases where the speaker s evidence was indirect but she did not share it. A natural second thought is that Support reduces to a requirement to assure your interlocutors that Indirectness is satisfied. But this approach is not plausible, for a few reasons. First, in most of the cases given above that are felt to be infelicitous without an argument Patch in her box, Sarah in her windowless office building, the Russian safe-house there no particular reason to worry that the speaker s evidence might not be indirect. Second, it is not generally true that whenever a formulation is constrained by a form of Indirectness, the speaker must habitually share her evidence in order to reassure her interlocutors that it satisfies the constraint in question. We have seen this in (21) with apparently, which is governed by an Indirectness constraint, but which doesn t require a shared argument; likewise, weaker epistemic modals, like might, probably, and should, are governed by an Indirectness constraint (as von Fintel and Gillies (2010) emphasize), but, as we saw in (16) (and the corresponding experimental results), do not come with a Support constraint. Likewise, Murray (2014) observes that grammatical evidential markers for indirectness do not give rise to any obligation to share one s evidence. And from a more theoretical standpoint, it is hard to see why an Indirectness constraint would directly yield an obligation to share one s evidence. We are generally charitable in assuming that speakers are complying with felicity conditions. For instance, if Indirectness were encoded as a presupposition, then, on a standard approach to presuppositions, it will be required that it be common ground that the speaker s evidence for the prejacent is indirect. But in general interlocutors are often happy to accommodate presuppositions (Lewis, 1979; Stalnaker, 2002). There are caveats to this: for instance, interlocutors generally will not accommodate presuppositions which involve anaphoric content (Kripke, 2009), address a question under discussion, or contain noteworthy information (Stalnaker, 1974, 2002). But these caveats do not seem to apply in the present case. To derive Support from Indirectness, we would need an explanation of why interlocutors are not in general willing to accommodate that Indirectness is satisfied. The most important problem with the second strategy, then, is that there does not appear to be a promising way to derive 13

Support from Indirectness. The second problem with the second strategy is that explaining Indirectness itself has turned out to be quite tricky: both main extant explanations have drawbacks which I will briefly survey here. I will not aim to argue decisively against those approaches, but rather to say enough to suggest that, even if we could reduce Support to Indirectness, there would remain open questions to address before we would have a satisfactory solution to Karttunen s Problem. The first main approach to explaining Indirectness is pragmatic. On this approach, an assertion of Must p proposes a weaker update than an assertion of p. By choosing the weaker update, the speaker signals that her evidence for p is too weak to merit an assertion of p. Thus we can conclude that the speaker s evidence for p is indirect, since direct evidence would have merited an assertion of p. 10 This approach seems obviously correct for capturing the correlate to Indirectness for weaker modals like might, probably, and epistemic should and ought. Assertions involving one of these (unembedded) modals are uncontroversially weaker than the corresponding non-modal assertions, and thus this account provides a natural explanation of the corresponding indirectness inference. Nor, in those cases, does a requirement for an argument arise, as we have seen so there is no question about how to extend this account of Indirectness to an account of such a requirement. But it is not clear that this approach extends equally well to the indirectness of must, because as von Fintel and Gillies (2010, 2018) have forcefully argued the assumption that Must p is weaker than p is at odds with intuitions about a broad range of data involving must. Those intuitions instead seem better captured by Pragmatic Strength: Pragmatic Strength: An assertion of Must p makes a proposal which is just as strong as an assertion of p. I will follow Stalnaker 1978 in assuming that an assertion of p is a proposal to make the common ground entail p; given that assumption, Pragmatic Strength says that an assertion of Must p is as strong as an assertion of p in that both are proposals to make the common ground entail p. In other words, Pragmatic Strength says that conversants do not leave open the possibility that p is false after accepting Must p : to accept the latter is, inter alia, to accept the former. To see the motivation for Pragmatic Strength, consider the contrasts in (22): (22) [Detective A: The gardener must be the murderer. Detective B, responding:] a. I concur. Let s arrest him. b.??i concur. Moreover, I ve discovered that the gardener is the murderer! c.??i concur. Let s bring him and the butler in to see if we can pin down which of them actually is the murderer. 10 The classic source of this approach is Karttunen 1972; Veltman 1985 and Kratzer 1977, 1981 give semantically weak semantics for must which provide a basis for pragmatically weak accounts. 14

Pragmatic Strength explains the infelicity of (22-b) as a response to Detective A: if Pragmatic Strength is true, then p adds nothing over and above Must p, accounting for the infelicity of sequences of the form Must p. Moreover p. And, likewise, Pragmatic Strength explains the infelicity of (22-c): once a group of interlocutors accepts Must p, then, if Pragmatic Strength is right, they should no longer leave open the possibility that p is false. By contrast, the infelicity of these sequences is hard to explain if Pragmatic Strength is false: if an update with Must p leaves it open that p is false, then it seems like (22-b) and (22-c) should be perfectly coherent. This point can be brought out clearly by contrasting (22-b) and (22-c) with variants which use weaker modals which uncontroversially do not satisfy Pragmatic Strength, Suppose that, instead of saying must, Detective A said The gardener is [probably/most likely/almost certainly] the murderer. Then the responses in (22-b) and (22-c) become perfectly felicitous. This is, again, exactly what we would expect if Pragmatic Strength holds for must, since it uncontroversially fails to hold for probably, most likely, almost certainly, and so on; and the contrast would be puzzling if must were pragmatically weak. 11 Pragmatic Strength can also be motivated, following von Fintel and Gillies 2010, based on the infelicity of conjunctions of Must p with conjuncts which propose to leave open the possibility that p is false, as in (23): (23) a. #The gardener must be the murderer, but there s some chance that he isn t. b. #The gardener must be the murderer, but he might not be. c. #The gardener must be the murderer, but let s leave open the possibility that he s not. d. #The gardener must be the murderer, but the butler is also a possibility. e. #The gardener must be the murderer, but it s possible he s not. f. #The gardener must be the murderer, but I don t know whether he is. g. #The gardener must be the murderer, but I don t know that he is. The infelicity of these variants is, again, explained straightforwardly by Pragmatic Strength. If updating with Must p entails an update with p, then it will be incoherent to propose an update with Must p together with a proposal to leave open that p is false, as in (23-a) (23-e). And, likewise, assuming that one should only propose an update with p if one knows p (as evidenced by Moore s paradox (Moore, 1942); see Williamson 2000 for recent discussion), Pragmatic Strength accounts for the infelicity of (23-f) (23-g). By contrast, it is hard to see how we would explain the infelicity of the variants in (23) if must is not pragmatically strong. 12 11 Indeed, it seems like for any n < 1, there is a clear contrast in this respect between There is an n% chance that p versus Must p. This seems like a particular problem for degree semantics (like Lassiter (2016) s) which predicts these to be Strawson-equivalent when n is sufficiently high. 12 Lassiter (2016) adduces some naturalistic sequences of the form Must p; possible not p, and nearby variations, which he argues are felicitous, contrary to my claim here. I find the data unconvincing, though I do not have space to discuss them in detail here. I believe that, in each case, the intended parse is not of the form Must p; possibly not p. The principle argument for this is that, in every case, must can be eliminated without sacrificing 15

All these considerations thus speak in favor of Pragmatic Strength, and at least suggest to me that Pragmatic Strength should be the default hypothesis. The present approach to Indirectness, which rejects Pragmatic Strength, incurs an as-yet unpaid debt: accounting for the striking data in (22) (23). If Pragmatic Strength is correct, however, then of course the present derivation of Indirectness does not work. 13 The main alternative explanation of Indirectness, due to von Fintel and Gillies (2010), 14 accepts Pragmatic Strength, and posits that epistemic modals lexically encode that the speaker s evidence is indirect as a semantic presupposition. This approach is motivated by, and avoids, the objection just given to the pragmatic approach. But this approach has its own drawbacks. The most serious of these, pointed out by Ippolito (2017), is that this approach does not make the right predictions about the projection of Indirectness from sentences which embed epistemic modals. I will not rehearse this point, which is somewhat complicated but strikes me as quite serious, here. 15 My present aim, again, is not to close the door on either of the extant approaches to Indirectness, but rather to make the points, first, that both leave Support unexplained; and, second, that both have (perhaps serious) drawbacks; which together suggest that an alternative approach is worth exploring. 3.2 From Support to Indirectness In the rest of this section, I explore just such a strategy, arguing that we can derive Indirectness from Support. In brief, the idea is as follows. First, Pragmatic Strength says that an assertion coherence. If the intended reading were Lassiter s, the results without must would have the form p and possibly not p, which are uncontroversially incoherent (see Wittgenstein 1953; Groenendijk et al. 1996; Gillies 2001; Yalcin 2007). In any case, the comparison without must suggests that these cases do not evidence a contrast in strength between must -claims and non-modal claims. Lassiter also reports an experiment in which participants are presented with a raffle scenario, and then asked to evaluate Bill did not win the raffle, Bill must not have won the raffle, It is possible that Bill won the raffle, and so on. Participants agreed with these three claims 69%, 58%, and 92% of the time, respectively. As Lassiter notes, these results are consistent with Must p entailing p (and thus with Pragmatic Strength), since participants were just as inclined to accept p as they were to accept Must p. 13 Pragmatic Strength is distinct from the strictly stronger principle that Must p entails that contextually relevant agents know p (which Lassiter (2016); Giannakidou and Mari (2016) argue against), and from the strictly stronger principle that Must p entails p (which Lassiter leaves open). Giannakidou and Mari (2016, 2017) defend an obligatorily weak view, on which Must p is not only compatible with lack of knowledge of p, but in fact entails that the speakers do not have complete knowledge of p. This, however, strike me as untenable. If this were correct, then sequences of the form Must p, and I know p for sure, and nearby variants, should be infelicitous, but they are not, as witnessed by the felicity of sequences like (24): (24) John must be at home; I [am completely sure/am certain/know for sure] he s there, because he s bedridden and cannot leave on his own. Goodhue (2017) similarly argues that Must p is felicitous only if p is not known, which likewise seems to predict that (24) will be infelicitous, contrary to fact. (In places Goodhue seems sympathetic to the idea that this constraint is defeasible; the present point of course does not tell against that view.) 14 And since (at least partly) endorsed and elaborated in Kratzer 2012a, Matthewson 2015, Lassiter 2016. 15 See also Sherman 2018; Matthewson 2015 for further discussion of criticisms of the lexical approach. 16

of Must p is a bid to update the common ground with p. Support says that it is a proposal to do so on the basis of an argument Γ. General principles concerning redundancy entail that p should not follow from Γ in a way that is mutually recognized to be obvious. Finally, speakers are generally obligated to give their best argument for p if they re giving an argument for p at all. It follows that, in order for an assertion of Must p to be felicitous, p should not follow in a mutually obvious way from the best argument a speaker of Must p has for p. In short, an assertion of Must p is a proposal to accept p on the basis of a shared argument, and this is the kind of proposal one should make only when that argument leaves some epistemic space between its premises and conclusion. The first step in our derivation is the assumption, defended in 3.1 above, that an assertion of Must p is pragmatically strong, in the sense that it is, inter alia, a proposal to update the common ground with p. The second step is to note that in general, when a speaker gives an argument in support of p with the intention of getting her interlocutors to accept p on the basis of that argument, the argument in favor of p must be non-redundant in some sense. Compare the two variants in each of (25) and (26): (25) a. I put Patch in her box this morning, and no one has let her out. So she s in her box. b.??i see Patch in her box. So she s in her box. (26) a. I ve just read a CNN report that says Clinton has amassed a majority of pledged delegates and superdelegates. So Clinton will clinch the Democratic nomination! b.??i ve just read a CNN report that says Clinton will clinch the Democratic nomination. So Clinton will clinch the Democratic nomination! (25-b) strikes me as objectionable; there is something pedantic or redundant about it. Likewise for (26-b), unless there is some salient doubt about the veracity of CNN. By contrast, (25-a) and (26-a) are fine. The difference seems to be that in (25-a) and (26-a), there is enough space left between the argument in the first sentence and its conclusion in the second that its conclusion is not felt to be redundant. This intuition can be regimented as a norm against redundant assertions, along the following lines: Non-Redundancy: A proposal to update the common ground with p on the basis of an argument Γ is infelicitous if p follows from Γ in a way that is mutually recognized to be obvious. In the next section I will further explore this principle. Note for the present, however, that Non- Redundancy nicely captures the contrast between (25-a) and (25-b), given our intuitive (albeit vague) notion of what it is for an inference to be mutually recognized to be obvious. The first is acceptable, since there is some epistemic space between the premises having put Patch in 17

her box in the morning, together with no one else having let her out and the conclusion that Patch is in the box (epistemic space filled by background assumptions about Patch s ability to get out on her own, etc.). The second is not, since it does follow in a mutually obvious way from seeing Patch in her box that she is in her box. Similar considerations apply to the contrast between (26-a) and (26-b). Note that Non-Redundancy, of course, does not forbid post hoc justification for an assertion with a redundant argument; it is perfectly fine to justify oneself, if challenged, with something like Because I saw it. What Non-Redundancy forbids is making an initial bid to update the common ground with p on the basis of an argument from which p follows in a mutually obvious way. Nor does Non-Redundancy forbid asserting p when p follows from your own private evidence in a mutually obvious way; see 3.3 for more discussion. Finally, note that Non- Redundancy is defeasible, as I discuss further in 5.3. The last step in our derivation says that a speaker must give the best argument for p that she has, if she s giving an argument for p at all. To see the plausibility of this constraint, consider (27): (27) [John was at the Red Sox game and knows on this basis who won. He also read about the game in the Boston Globe.] a. [Max:] Who won the game? b. [John:]?? The Red Sox, according to the Globe. If John intends (27-b) to answer Max s question, then there is something strange about it; we expect John to give his strongest evidence for the claim that the Red Sox won. In general, speakers are required to share the best piece of evidence they have for a claim, if they are sharing evidence at all. This follows naturally from a broadly Gricean vantage point on conversational dynamics: in (27-b), John is violating Grice s Maxim of Quantity by failing to make his contribution as informative as is required (for the current purposes of the exchange) (Grice, 1989). More precisely, the lesson of cases like this is a corollary of the Maxim of Quantity which I call Strongest Evidence: 16 Strongest Evidence: When a speaker gives an argument for a claim, she must provide the best piece of evidence she can. We can now put these pieces together to derive Indirectness from Support. Support says that an assertion of Must p is felicitous only if there is a shared argument for p. Pragmatic Strength says that an assertion of Must p is a proposal to update the common ground with p. 16 See Faller 2012 for more careful discussion of how this kind of reasoning would go. To spell out Strongest Evidence in more detail, we need to be able to access a scale of evidential strength, according to which, say, direct perceptual evidence counts as stronger than any kind of testimonial evidence on this point see also Faller 2001. Strongest Evidence is of course in tension with the aim of brevity, and ordinary conversational moves presumably aim to strike a balance between these. 18

It is natural to therefore assume that an assertion of Must p is thus a proposal to update the common ground with p on the basis of a shared argument for p. According to Non-Redundancy, p must not follow from that argument in a mutually obvious way. According to Strongest Evidence, that argument must constitute the best evidence the speaker has for p. It follows that in order for a speaker to be able to felicitously assert Must p, p cannot follow in a mutually obvious way from the speaker s best evidence for p. In other words, the speaker s best evidence for p must be indirect, in the sense of indirectness relevant to evaluating whether an argument is felt to be redundant. In sum: in asserting Must p, the speaker has to ensure there is a shared argument which represents her best evidence for p, and yet is not so strong that it makes the must -claim sound redundant. Thus p can t follow in a mutually obvious way from her best evidence for p. No parallel constraint follows for non-modal claims since Support requires only that must -claims be supported by an argument and thus Indirectness follows from Support, plus Pragmatic Strength, Non-Redundancy, and Strongest Evidence. 3.3 Non-Redundancy Before turning to the question of how to predict Support, I will say more about the conversational architecture that underlies Non-Redundancy (in this subsection), as well as the predictions made by the present derivation of Indirectness (in the next subsection). More could be said about each of the assumptions I made in the last section, but Non-Redundancy is the one most in need of further explanation here, since a central upshot of my account is that the signal of indirectness associated with must reduces to judgments about redundancy. Saying more about redundancy will help us evaluate the theoretical foundations and empirical ramifications of this claim. Non-Redundancy forbids updating the common ground with p on the basis of an argument Γ when p follows from Γ in a way mutually recognized to be obvious. Non-Redundancy follows from two further claims. The first is that a proposal to update the common ground with p on the basis of an argument Γ is a proposal to update the common ground with Γ and then with p. The second is that one should not propose a series of updates if, should they all be accepted, the final update will be judged to be redundant. The first of these claims is fairly self-evident. The second requires further exploration. It has its foundation in the more general idea that there is something wrong with redundant assertions, along the following lines: Common Ground Entailment: Don t assert p if p is entailed by the common ground. 17 This norm is very natural if we think of conversations as cooperative enterprises whose main goal is information transfer. Asserting what is already common ground does not serve that goal. 17 See Stalnaker 1974, 1978, 1973. Some version of this norm applies at the subsentential level as well; see e.g. Schlenker 2008, 2009, Mayr and Romoli 2016. 19